I can see not everyone has done one of these, but I thought it'd be helpful, for me if for no one else. ♥
Basics
Kairi is sixteen, and post-KHII in terms of timeline. She looks more or less the same as in KHII, although she has gained a few inches in height and grown her hair out a little more since then. Separated from Sora on the day he went Anti Form, she has been looking for him ever since.
Because she is post-KHII, Kairi and Namine have merged. Namine does not "come out" the way some Nobodies do, but if you catch Kairi talking to herself, she was probably talking to the other girl in her heart. It is because of Namine that Kairi was able to traverse the worlds "alone" -- her shadow opened the dark corridors for her. (Doing this takes a lot out of Namine, however, and so Kairi cannot "warp" or anything like that. Two full days of rest were needed between jumps, and Kairi won't be making a habit of it any time soon.)
Kairi is very slightly wary, on a gut level, of people who spend too much time in darkness -- it makes her nervous. But this is literally light and darkness, not good and bad -- if you're playing a demon from a sun-scorched dimension, she's as likely as anyone else to fall for your act. Batman, on the other hand, might unsettle her.
In combat
Kairi does not really have a keyblade of her own, but after long instruction from both Sora and Riku, she has figured out the trick to "borrowing" a little of someone else's, and so took half of Riku's with her (as well as his Last Radiance keychain) when they parted ways. Kairi strongly suspects that any other Princess of Heart could do the same, because of their special connection to the keyblade.
However, the instant Kairi stepped into the Nexus, her connection with Riku snapped, and the borrowed keyblade vanished. If she is to summon it again, she will have to first find someone else who wields one (another Riku, Sora, Roxas, or Mickey).
So, while she would ordinarily be able to hold her own, Kairi is, for all intents and purposes, a noncombatant now. She is well-aware of this, and will strive not to "start anything" -- because while she's deeply touched to have people who care enough for her to rescue her, she really hates being a burden on them.
Miscellaneous
If Sages were a Dungeons and Dragons-style RPG, Kairi would come equipped with a special ability called "See With Your Heart" and you'd use it with a D20.
In other words, if you've been LOL'd in some fashion -- changed into a woman, your worst enemy, a carrot, or a five-year-old -- Kairi has a better than average chance of recognizing you anyway. It will take her between a few seconds to five minutes, and she has to know you pretty well, although she'll probably notice you're not who you should be even if you've never met her.
Let me know if, for some reason, you really want her not to know! I'm flexible. ♥